Likelihood-based estimation

Question 1

Define the likelihood and log likelihood functions

Answer 1

pg 15 (actually look)

Question 2

Define MLE

Answer 2

Maximum likelihood estimator

L_n(θ^) = max_{θ∈Θ} L_n(θ)

Question 3

What does it mean to say the MLE has the property of invariance?

Answer 3

if θ^ is the MLE of θ and g is an arbitrary function of θ, then g(θ^) is an MLE of g(θ)

Question 4

State the score function of θ

Answer 4

pg 19

Question 5

Define the Fisher information matrix

Answer 5

pg19

Question 6

If X = (X1 , … , Xn) with Xi

i.i.d. random variables, state the Fisher information of X

Answer 6

I_n (θ) = n I(θ)

Question 7

State the Cramer-Rao lower bound and Proposition 2.2

Answer 7

pg 21 and pg 23